# Equations of tangents through point (curve)

• Jun 17th 2008, 12:52 AM
theowne
Equations of tangents through point (curve)
Determine the exact equations of the tangents to the curve which pass through point P

curve = (8-x)^(1/2)
point = 5,2

I'd like to see how you would solve this. What I tried to do is set the variables of the point as: a, (8-a^(1/2))
and the slope would be
-1 /( 2(8-x)^(1/2) )

Is this right? Putting this into the y-y0 = m (x-x0) seems to get messy...
• Jun 17th 2008, 01:03 AM
Moo
Hello,

Quote:

Originally Posted by theowne
Determine the exact equations of the tangents to the curve which pass through point P

curve = (8-x)^(1/2)
point = 5,2

I'd like to see how you would solve this. What I tried to do is set the variables of the point as: a, (8-a^(1/2))
and the slope would be
-1 /( 2(8-x)^(1/2) )

Is this right? Putting this into the y-y0 = m (x-x0) seems to get messy...

$f'(x)=\frac{-1}{2(8-x)^{1/2}} \quad \leftarrow \quad \text{Right !}$
Find $f'(5)$
$y=f'(5)(x-5)+\underbrace{f(5)}_{=2}$